Hi Bhujiko and welcome to 3FC! Congratulations on starting your running program!
There are some common fallacies that get tossed around about muscle building that aren't true but they sure can be confusing.
If you don't mind, let me take a stab at some:
1. Muscle doesn't weigh more than fat. If you gain a pound of muscle, your scale will go up a pound, but only a pound. If you gain a pound of fat, your scale will likewise go up a pound. When people say muscle weighs more than fat, they're trying to say is that muscle is smaller than fat, so a pound of fat takes up less space than a pound of muscle (yay!) But it's not an explanation for the scale going up.
2. Running isn't muscle building exercise, so you haven't gained muscle from starting a running program. Running is cardiovascular exercise -- it burns calories, and can strengthen muscles and build endurance -- all fantastic! But to add muscle, you need to be working your muscles against resistance, which is weight training/resistance training, not cardio.
3. Muscle doesn't replace fat. They're completely different parts of your body. You can lose fat, you can lose muscle, you can gain fat and/or muscle -- but muscle gain and fat loss are independent of each other.
4. It takes many months of serious weight training and a good nutrition program in order for a woman to gain a few pounds of muscle. It's not easy and you're right, it could never happen in a week.
So what happened to you?
It's very, very common to see the scale go up when an exercise program is started. Usually it's because sore muscles retain water and what you see is a temporary water weight gain on the scale, which is nothing to worry about! Sometimes it can also be us eating more to compensate for exercise, so you might want to track your calories closely and see if this is happening to you.
Here's an article you might want to check out: Working Out — And Gaining Weight?
Bottom line: unless you've been eating a lot more calories, what you're seeing on the scale is most likely a temporary water weight blip. Hang in there -- you're doing great!